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XmR Individuals Chart Formulas

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The XmR (Individuals and Moving Range) Chart can help you evaluate a process when there is only one measurement and they are farther apart: monthly postage expense and so on.

Formulas for the Moving Range and Individuals chart in QI Macros.

Moving Range Chart formula

Individuals X Chart formula

k = number of data points

for n=2 observations (moving range is calculated from two samples, the present minus the previous value)

D₄ = 3.267

D₃ = 0

E₂ = 2.660

Conforms with ANSI/ASQC B1, B2, B3 1996

NOTE: It is possible to have negative limits on an XmR Chart.

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QI Macros XmR Charts employ the Nelson Rule for Moving Range

"Any moving range (Ri) greater than 3.5*Rbar should be removed from the average moving range calculation."

In example below, point 20 (46.50) is greater than 3.5*11.14 (original Rbar), so it will be removed from Rbar Calculation which changes Rbar to 9.73 and UCL/LCL for both the X and R charts. 

Source: Control Charts for Individual Measurements, Lloyd S. Nelson, Journal of Quality Technology, Vol. 14, No. 34, July 1982.

Process: Calculate, plot, and evaluate the range chart first. If it is "out of control," so is the process. If the range chart looks okay, then calculate, plot, and evaluate the X Chart.

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Other Resources

• Create a XmR Individuals Chart in Excel using QI Macros
• XmR Individuals Chart Video
• XmR Individuals Chart Template in Excel

The XmR Individuals chart is just one of the tools included in the QI Macros SPC Software for Excel.

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